# Fun on the First Day Back

I’ve decided to do something new for the first day back after break.  Instead of doing the typical “hand back the exam, go over the difficult questions,” I’ve decided to shake things up.

For my algebra 1 and algebra 2 classes, I’m going to follow the following game plan for the first days back.

• Brain CRUSHER (30 minutes)
• Hand back exams so students can go over (10 min)
• “Exam Redux” homework

Nowhere in there will I “go over” an exam problem on the board.  Instead, the problems I think we need to review will be built into homework.

My main goal is to build in a fun, inquisitive and engaging return to math class without having to hold the students accountable to much aside from thinking about a perplexing topic.

For algebra 1, I’ll give the “1=2” proof.  One of my greatest life regrets was not taking a picture of this proof when I saw it written on the bathroom stall in the math department building in college.  Oh, what could have been 🙂

```     a = x            [true for some a's and x's]
a+a = a+x          [add a to both sides]
2a = a+x          [a+a = 2a]
2a-2x = a+x-2x       [subtract 2x from both sides]
2(a-x) = a+x-2x       [2a-2x = 2(a-x)]
2(a-x) = a-x          [x-2x = -x]
2 = 1            [divide both sides by a-x]```

For algebra 2, I’ll pose a simpler question but one I expect to produce some interesting discussion:

0.9999999999999999… = 1

True of false?

I’ll be able to finish this discussion by showing Vi Hart’s video, too!

Much better than your normal “lets go over exam questions,” don’t you think?  Any other good brainteasers/perplexing “math only” questions?  By math only, I’m meaning just purely mathematical questions.  I’ve been inspired by Dan’s post on engaging fake world math and am looking for ways to inject more of it into my classes.